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GO Classes 2023 | Weekly Quiz 7 | Question: 10

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Consider a set $\text{A} = \{ a,b,c,d,e,f,g \}.$

Consider the following partition $\text{P}$ of set $\text{A}:$

$\text{P} : \{ \{a,b\} , \{c\}, \{d\}, \{e,f,g\} \}$

We define an equivalence relation $\text{R}$ on set $\text{A}$ such that the set of equivalence classes of $\text{R}$ is exactly the same as partition $\text{P}.$

What is the cardinality of relation $\text{R}?$
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Given equivalence classes are – E1 = {a,b}, E2 = {c}, E3 =  {d}, E4 = {e,f,g}.

| R | = | E1 |^2 + | E2 |^2 + | E3 |^2 + | E4 |^2

since, all elements of an equivalence class are related to all other elements of that class and no element is related to some element of other equivalence class.

| R | = 2^2 + 1^2 + 1^2 + 3^2 = 15

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